Solution of a Terminal Control Problem under State Constraints

Trajectory planning for mechanical systems in the presence of dynamic obstacles

“…Motion planning problems are of high importance for various robotic systems and the last decades have witnessed a lot of attention paid to this area of research among control theorists and engineers. Meanwhile, typical approaches to reference trajectories construction are based on using time polynomials which proved to be an effective tool, e.g., for differentially flat dynamical systems (see [1,2,3,4,5,6,7,8,9]). Numerical optimization procedures to meet geometrical, velocity and acceleration constraints are discussed in [1,6,7].…”

“…Numerical optimization procedures to meet geometrical, velocity and acceleration constraints are discussed in [1,6,7]. Some analytical ideas of constrained trajectory planning for mechanical systems can be found e.g., in the monograph [2] and in papers [8,9]. In [8,9] time polynomials based point-to-point motion planning for a chain of second-order controlled subsystems is proposed to meet the state constraints by proper selection of the time of motion.…”